This paper is used to solve the systems of linear Volterra integral equations by means of the combined sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective. Mathematics Subject Classification (2010): 45D05, 34A12, 34C20, 65R10
Topics
Integral equations
REFERENCES
1.
A. M.
Wazwaz
, Linear and nonlinear integral equations methods and applications
, Springer
, higher education Prees
, (2011
).2.
J.
Biazar
, M.
Eslami
, and M.
Islam
, Differential transform method for special systems of integral equations
. J. of Soud. U. Sci.
24
, 211
–214
(2012
).3.
Gu
, Z.
Chebyshev spectral collocation method for system of nonlinear Volterra integral equations
. Numer Algor
83
(2020
), 243
–263
. 4.
G. K.
Watugala
. Sumudu transform: a new integral transform to solve differential equations and control engineering problems
. Int. J. Math. Edu. Sci. Tech.
24
(1
) 35
–43
(1993
).5.
G.
Adomian
, Nonlinear Stochastic Systems Theory and Applications to Physics
, Kluwer Academic Publishers
, Dordrecht
, (1989
).6.
G.
Adomian
, Solving Frontier Problems of Physics: The Decomposition Method
, Kluwer Academic Publishers
, Dordrecht
, (1994
).7.
Waleed
Al-Hayani
, Luis
Casasús
, The Adomian decomposition method in turning point problems
, Journal of Computational and Applied Mathematics
177
, 187
–203
(2005
). doi:8.
Afrah S.
Mahmood
, Luis
Casasús
, Waleed
Al-Hayani
, The decomposition method for stiff systems of ordinary differential equations
, Applied Mathematics and Computation
167
, 964
–975
. (2005
). DOI:9.
Afrah S.
Mahmood
, Luis
Casasús
, Waleed
Al-Hayani
, Analysis of resonant oscillators with the Adomian decomposition method
, Physics Letters A
357
, 306
–313
(2006
). DOI:10.
Hongqing
Zhu
, Huazhong
Shu
, Meiyu
Ding
, Numerical solutions of two-dimensional Burgers’ equations by discrete Adomian decomposition method
, Computers and Mathematics with Applications
60
, 840
–848
. (2010
). DOI:11.
Yasir
Khan
and Waleed
Al-Hayani
, A Nonlinear Model Arising in the Buckling Analysis and its New Analytic Approximate Solution
, Z. Naturforsch.
68a
, 355
–361
, (2013
). DOI:12.
Jun-Sheng
Duan
, Temuer
Chaolu
, Randolph
Rach
, Lei
Lu
, The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations
, Computers and Mathematics with Applications
66
, 728
–736
(2013
). doi:13.
I.
Hashim
, O.
Abdulaziz
, S.
Momani
, Homotopy analysis method for fractional IVPs
, Communications in Nonlinear Science and Numerical Simulation
14
, 674
–684
(2009
). doi:14.
Waleed
Al-Hayani
, Laheeb
Alzubaidy
, Ahmed
Entesar
, Solutions of Singular IVP’s of Lane-Emden type by Homotopy analysis method with Genetic Algorithm
, Appl. Math. Inf. Sci.
11
(2
), 1
–10
(2017
). 15.
Waleed
Al-Hayani
, Laheeb
Alzubaidy
, Ahmed
Entesar
, Analytical Solution for the Time-Dependent Emden-Fowler Type of Equations by Homotopy Analysis Method with Genetic Algorithm
, Applied Mathematics
8
, 693
–711
, (2017
). 16.
Jun-Sheng
Duan
, Temuer
Chaolu
, Randolph
Rach
, Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach–Adomian–Meyers modified decomposition method
, Applied Mathematics and Computation
218
, 8370
–8392
, (2012
). doi:17.
Waleed
Al-Hayani
, Adomian decomposition method with Green’s function for solving twelfth-order boundary value problems
, Applied Mathematical Sciences
9
(8
), 353
–368
, (2015
). 18.
A. S. V. Ravi
Kanth
and K.
Aruna
, He’s homotopy-perturbation method for solving higher-order boundary value problems
. Chaos Soliton Fract.
41
(4
), 1905
–1909
, (2009
). 19.
A.S.V. Ravi
Kanth
and K.
Aruna
, Variational iteration method for twelfth-order boundary-value problems
. Comput. Math. Appl.
58
(2009
), 2360
–2364
. 20.
G. K.
Watugala
. Sumudu transform: a new integral transform to solve differential equations and control engineering problems
. Int. J. Math. Edu. Sci. Tech.
24
. (1993
).21.
Pakhshan M. A.
Hasan
, Nejmaddin A.
Sulaiman
, Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations
, Iraqi Journal of Science
, 61
(2
), 409
–415
, (2020
). DOI: 22.
Z. K.
Eshkuvatov
, F. S.
Zulkarnain
, N. M. A. Nik
Long
and Z.
Muminov
, Modified homotopy perturbation method for solving hypersingular integral equations of the first kind
, Springer Plus
5
, 1473
(2016
). DOI 23.
Waleed
Al-Hayani
and Omar Mudhar
Kashmola
, Adomian Decomposition Method for Solving the Singularly Perturbed Volterra Integral Equations
, Mathematical Sciences Letters
6
(2
), 1
–10
(2017
). 24.
Adomian
, Nonlinear Stochastic Systems Theory and Applications to Physics
, Kluwer Academic Publishers
, Dordrecht
, (1989
).25.
Dr. Omer M. A.
Al-Faour
, Rostam K.
Saeed
, Solution of a system of linear voltera integral and integro-differential equations by spectral method
, Al-Nahrain University journal for Science
, (2006
).26.
M.
Rabbani
, K.
Maleknejad
, N.
Aghazadeh
, Numerical computational solution of the Volterra integral equations system of the second kind by using an expansion method
, Applied Mathematics and Computation
187
, 1143
–1146
. (2007
). doi:27.
M.I.
Berenguer
, D.
Gámez
, A.I.
Garralda-Guillem
, M. Ruiz
Galán
, M.C. Serrano
Pérez
, Biorthogonal systems for solving Volterra integral equation systems of the second kind
, Journal of Computational and Applied Mathematics
235
, 1875
–1883
, (2011
). doi:28.
V.
Balakumar
, K.
Murugesan
, Single-Term Walsh Series method for systems of linear Volterra integral equations of the second kind
, Applied Mathematics and Computation
228
, 371
–376
(2014
). 29.
Waleed
Al-Hayani
, Solving nth-order integro-differential equations using the combined Laplace transform-Adomian decomposition method
, Applied Mathematics
4
, 882
–886
, (2013
). doi:30.
Fethi B. M.
Belgacem
, Ahmed A.
Karaballi
, and Shyam l.
Kalla
, Analytical investigations of the Sumudu Transform and applications to integral production equations, Mathematical Problems in Engineering
3
103
–118
. (2003
). URL:31.
Fethi B. M.
Belgacem
and Ahmed A.
Karaballi
, Sumudu Transform fundamental properties investigations and applications
, Journal of Applied Mathematics and Stochastic Analysis
, Volume 2006
, Article ID 91083, Pages 1
–23
. DOI
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.
